Don't you hate it when things stop working in the cold. Bring it in somewhere warm, charge up the battery. Make sure it will hold a charge. Might take overnight to charge it up. Test it under load. Ie, cranking motor or with lights on. If its ok, Look over the wiring to make sure everything is in place. I'm assuming a GM type alternator: Check for 12volts at the two terminals (bat and red wire to two terminal plug). Make sure the terminals are not corroded or loose. The dark wire that goes to the two terminal plug also gets 12 volts from the key on power on the harness, but it is through a resistance wire to prevent it from keeping the ignition running as it puts out alternator voltage once it is operating. You can do a temporary hookup straight to your battery just to test it. Start it up and see if there is an increase in voltage at the battery. It should go up to or above 14 volts with the engine running, compared to around 13 on a charged battery. If the wiring harness looks good and it still doesn't charge, then remove the alternator and take it into a shop to have it tested.